One of my favourite bands of the last decade is Hamilton Yarns, who are rarely amplified or use microphones at all. Even that acoustic guitar is only gently picked, never aggressively strummed, and the vocals are very soft. There is generally muted trumpet, but that's as loud as it gets. This probably all sounds very twee, but they're quite experimental; I think I once described them as a pastoral Faust playing the music of Vernon Eliot.